Triangle Area Calculator
Find a triangle’s area from its three side lengths with Heron’s formula — no height needed.
How it works
Area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) ÷ 2
Heron’s formula finds the area from the three sides alone — no height or angle required. First compute the semi-perimeter s, then multiply s by its distance from each side and take the square root. If the sides fail the triangle inequality (one side as long as the other two together), no triangle exists and the formula would go imaginary.
Worked example
Sides 5, 6 and 7: s = (5 + 6 + 7) ÷ 2 = 9. Area = √(9 × 4 × 3 × 2) = √216 ≈ 14.6969 square units.
Frequently asked questions
What if I know base and height instead of three sides?
Then the simpler formula A = ½ × base × height is quicker — the Area Calculator on this site handles that case directly.
Why do my three measurements give an error?
They break the triangle inequality: each side must be strictly shorter than the sum of the other two. Sides 2, 3 and 8 can’t close into a shape, because 2 + 3 < 8.
Does Heron’s formula work for right triangles too?
Yes, it works for every valid triangle. For a right triangle it just reproduces ½ × leg × leg — try 3, 4, 5 and you’ll get exactly 6.
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This calculator is for educational purposes. Double-check important results before acting on them.